Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20272659 | C2 | direct (N × H) |
| 32. C2×C42×C53 | C8 | semidirect |
| 64. C42×C53 | C2×C8 | semidirect |
| 127. C2×C53 | #1324 | semidirect |
| 141. C53 | C2×#1324 | semidirect |
| 158. C2×C42 | #88322 | semidirect |
| 194. C42 | C2×#88322 | semidirect |
| 251. C2 | #20272659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810349 | 2 |
| #20272659 | 2 |
| C2×C53×#382 | 2 |
| C2×#1324 | 53 |